Phi (Φ) can be determined for Cable 2 from:
[tex]tan^-1 (Fy/Fx).[/tex]
In trigonometry, [tex]tan^-1 (Fy/Fx)[/tex] represents the inverse tangent function, also known as arctan or atan.
This function is used to find the angle whose tangent is equal to the ratio of the y-component (Fy) to the x-component (Fx) of a vector.
By calculating the ratio Fy/Fx and applying the inverse tangent function, we can determine the angle phi (Φ) for Cable 2.
The value obtained from [tex]tan^-1 (Fy/Fx)[/tex] will represent the angle in radians.
It's important to note that the resulting angle phi (Φ) will provide information about the direction or inclination of Cable 2 based on the given vector components Fy and Fx.
In summary, to determine the angle phi (Φ) for Cable 2, we use the inverse tangent function, represented as[tex]tan^-1 (Fy/Fx),[/tex] which calculates the angle whose tangent is equal to the ratio of the y-component to the x-component of the vector.
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In ΔNOP, p = 70 inches, n = 97 inches and ∠O=163°. Find ∠N, to the nearest degree.
Answer:
10°----------------------
In ΔNOP, we are given:
p = 70 inches, n = 97 inches, ∠O = 163°Use the law of cosines to find side o:
o² = n² + p² - 2(np)cos(∠O) o² = 97² + 70² - 2(97)(70)cos(163°) o² = 27295.61o = 165.2Now, use the law of sines to find ∠N:
sin(∠N) / n = sin(∠O) / o sin(∠N) / 97 = sin(163°) / 165.2sin(∠N) = 97*sin(163°) / 165.2sin(∠N) = 0.17m∠N = arcsin (0.17)m∠N = 9.78° ≈ 10°So, ∠N is approximately 10°.
Write the slope-intercept form of the equation for each line.
Step-by-step explanation:
points on the line: (4, -2) & (-5, 3)
gradient of the line = -5/9
general equation for all straight lines: y = mx + c
substitute one coordinate and the gradient into the equation. 3 = (-5/9)(-5) + c
therefore, c = 2/9
so the general equation is y = (-5/9)x + 2/9
I need help with this problem
Answer:
please see answers below
Step-by-step explanation:
In a right-angled triangle, a ² + b ² = c ².
angles in a triangle add up to 180°.
Sine rule: a/SIN A = b/SIN B = c/SIN C
angle C = 90° (little square means 90).
if angle A is 30, then angle B must be 180 - 90 - 30 = 60°.
using the Sine rule:
a/Sin A = c/Sin C
multiply both sides by Sin A:
a = (c Sin A) / Sin C
= (12 Sin 30) / Sin 90
= 6.
so a = 6.
Using Pythagoras (In a right-angled triangle, a ² + b ² = c ²),
c² = a² + b²
b² = c² - a²
= 12² - 6²
= 144 - 36
= 108
so b² = 108
b = √108
angle B is correct
An aeroplane flies from a town X on a bearing of N45°E to another town Y, a distance of 200 km. It then changes course and flies to another town Z on a bearing of S60°E. If Z is directly east of X, calculate, correct to 3 significant figures, a the distance from X to Z by the distance from Y to XZ.
The distance from X to Z will be 386 km when rounded to 3 significant figures.
The distance from Y to XZ will be 141 km when rounded to 3 significant figures.
How to obtain the distancesTo obtain the distances, we need to extend the distances traveled by the airplane and this yields another triangular form. Angle Y = 105°, z = 200 km, and Z = 30°.
y/Sine Y = z/Sine Z
y/Sine 105° = 200/Sine 30°
y = 200 × 0.966/0.5
386 km to 3 significant figures
Also for the distance from Y to XZ,
We assume that the distance from Y to XZ is d
Sine 45°/1 = d/200
d = 200 sine 45°
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I need help with this Piece-Wise Function Please
With f(1), we're being given an x-value of 1.
Since 1 < 3 (and not ≥3) we need to use the first formula that is used when x<3.
f(1) = 1 - 2 = -1
If I have 7.55 how many dimes and quarters is it
Answer:
To convert 7.55 dollars into dimes and quarters, we need to make use of the fact that there are 10 dimes in a dollar and 4 quarters in a dollar. Here's how to do it:
Step-by-step explanation:
1. First, convert the dollar amount into cents: 7.55 dollars x 100 cents/dollar = 755 cents.
2. Next, use long division to find how many quarters are in 755 cents: 755 ÷ 25 = 30 with a remainder of 5.
3. The quotient of 30 tells us that we can use 30 quarters, which equals $7.50.
4. The remainder of 5 cents is less than a quarter, so we cannot use another quarter. Instead, we can use 1 dime, which is worth 10 cents.
Therefore, 7.55 dollars is equivalent to 30 quarters and 1 dime.
how many square are there in 384 sq ft
The number of squares that are in 384 sq ft is 0
How many square are there in 384 sq ftFrom the question, we have the following parameters that can be used in our computation:
Area expression = 384 sq ft
The above expression is an area expression
This means that it cannot be compared to quantities other then squares
The term "how many squares" is not an area expression
Hence, there are no squares in 384 sq ft
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A right triangle is removed from a rectangle to create the shaded region shown below. Find the area of the shaded region. Be sure to include the correct unit in your answer.
The area of the shaded region is equal to 45 square units.
How to calculate the area of a rectangle?In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:
A = LW
Where:
A represent the area of a rectangle.W represent the width of a rectangle.L represent the length of a rectangle.By substituting the given side lengths into the formula for the area of a rectangle, we have the following;
Area of rectangle = 8 × 6
Area of rectangle = 48 square units.
Since the opposite sides of any rectangle are congruent (equal), the legs of the right triangle can be calculated as follows;
L₁ = 8 - 5 = 3 units.
L₂ = 6 - 4 = 2 units.
Area of right triangle = 1/2 × 3 × 2
Area of right triangle = 3 square units.
For the area of the shaded region, we have:
Area of the shaded region = 48 square units - 3 square units.
Area of the shaded region = 45 square units.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
(08.01 MC)
Which of the following is the graph of f(x)=x²-5x +4?
Answer: C
Step-by-step explanation:
If I plugged in 0 for x, You get 4 for y. This is the y-intercept
(0,4)
The only graph that goes through (0,4) is C.
Find the inverse for: f(x) = 2x^2-3
Unless we restrict its domain, a quadratic function doesn't have the inverse.
Inequalities - Introduction
Answer:
n = 19
Step-by-step explanation:
2n > 36 ( divide both sides by 2 )
n > 18
and
5n < 100 ( divide both sides by 5 )
n < 20
so n > 18 and n < 20
thus n = 19
solve each compound inequality. -28 < -4r < 16
The solution to the compound inequality -28 < -4r < 16 is 7 > r > -4
How to determine the solution to the compound inequalityfrom the question, we have the following parameters that can be used in our computation:
-28 < -4r < 16
Divide through the inequality by -4
so, we have the following representation
-28/-4 < -4r/-4 < 16/-4
When the quotients are evaluated, we have
7 > r > -4
Hence, the solution to the compound inequality is 7 > r > -4
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A metal is composed of copper and zinc in the ratio 3:2 by volume. Find the volume of a piece of the metal which contains 42 cm³ of copper.
Answer:
70 cm³
Step-by-step explanation:
let the total volume be x
copper : zinc = 3:2
copper ==>
3/5 *x = 42
make x the subject if formula
x = 42*5/3
:. x = 70 cm³✅✅
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Segment RT has endpoints R(1,1) and T (-7, -2) what are the coordinates of the midpoint of RT?
James exercised for 2/5 of an hour and sandile exercised for 4/12 of an hour ? Who exercised for the longest time?
Answer:
The answer James
Step-by-step explanation:
James=2/5hours
J=2/5×60=2×12=24 minutes
Sandle=4/12×60=4×5=20 minutes
Cite at least 3
situations in your community where you can apply hypothesis testing. Then, just
choose one situation and:
1. Create a problem statement;
2. Formulate the null and alternative hypothesis;
3. Select the level of significance and sketch the rejection region; and
4. State the possible Type I and Type II errors.
In my community, there are several situations where hypothesis testing can be applied. Here are three examples: Traffic Flow Optimization, Recycling Program Assessment, and Crime Prevention Strategy Evaluation
What inform the selected situation?For the purpose of this response, let's choose Situation 1 (Traffic Flow Optimization) and go through the four steps.
1. Problem Statement: The local authorities want to determine if implementing a new traffic signal timing system will significantly reduce the average travel time for commuters passing through a busy intersection during peak hours.
2. Null Hypothesis (H0): The new traffic signal timing system has no effect on the average travel time for commuters passing through the intersection.
Alternative Hypothesis (H1): The new traffic signal timing system significantly reduces the average travel time for commuters passing through the intersection.
3. Level of Significance: α = 0.05
4. Rejection Region: The rejection region will depend on the specific test statistic used. Let's assume we are using a t-test to compare the mean travel time before and after implementing the new traffic signal timing system. In this case, we would calculate the t-statistic and determine the critical value(s) based on the degrees of freedom and the chosen level of significance. The rejection region would be in the tails of the t-distribution corresponding to the critical value(s).
Possible Type I Error: Rejecting the null hypothesis when it is actually true, indicating that the new traffic signal timing system is effective when it is not. In this case, it would mean concluding that the new system significantly reduces travel time when, in reality, it has no effect.
Possible Type II Error: Failing to reject the null hypothesis when it is actually false, indicating that the new traffic signal timing system is ineffective when it is actually effective. In this case, it would mean not detecting a significant reduction in travel time when the new system does indeed have a positive impact.
It's worthy of note that the specific test statistic and rejection region may vary depending on the nature of the data and the chosen statistical test. The above steps provide a general framework for conducting hypothesis testing in the given situation.
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Dada la circunferencia de ecuación x2+y2-2x+4y-4=0, hallar el centro
y el radio, luego grafique la circunferencia
The equation for the circle is
(x - 1)² + (y + 2)² = 9
Then the radius is 3 units and the center is (1, -2), the graph is on the image at the end.
How to find the center and radius of the circle?Remember that for an equation for a circle of radius R and center (a, b), the equation is:
(x - a)² + (y - b)² = R²
Here we have the equation of the circle:
x² + y² - 2x + 4y - 4 = 0
We need to complete squares, we will get:
(x² - 2x) + (y² + 2*2y) = 4
Now we can add in both sides (-1)² and (2)², then we will get:
(x² - 2x + (-1)²) + (y² + 2*2y + (2)²) = 4 + (2)² + (-1)²
(x - 1)² + (y + 2)² = 4 + 4 + 1
(x - 1)² + (y + 2)² = 9 = 3²
Then we can see that the center is (1, -2), and the radius is 3.
The graph of this circle is on the image at the end.
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In the figure below quadrilateral JKLM is similar to quadrilateral NPQR. Select All the true statements.
J
12
K
20
M
85°
100°
5y + 1
O&P = 50°
0 x = 2.
O&R=85*,
Oy = 3.
0 = 6.
L
R
8
Q
10
7
N
x +4
POSSIBLE
P
Answer:
x = 2∠R = 85°y = 3Step-by-step explanation:
Given quadrilaterals JKLM and NPQR are similar with K=100°, M=85°, JK=12, LM=(5y+1), MJ=20, RN=10, NP=(x+4), PQ=7, QR=8, you want to identify the true statments.
Relations
Corresponding angles are congruent, so we have ...
∠K≅∠P = 100°
∠M≅∠R = 85°
Corresponding sides have the same ratio. The larger : smaller ratio here appears to be 2 : 1.
JK : NP = 12 : (x+4) ⇒ x+4 = 6 ⇒ x = 2
KL : PQ = ? : 7 ⇒ KL = 14
LM : QR = (5y+1) : 8 ⇒ 5y+1 = 16 ⇒ y = 3
MJ : RN = 20 : 10 . . . . . establishes the ratio for the others
The true statements are ...
x = 2∠R = 85°y = 3__
Additional comment
It can be helpful to write a list of the specific correspondences (based on the similarity or congruence statement).
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Linda wants to save $900 to buy a TV. She saves $18 each week. The amount, A (in dollars), that she still needs after w weeks is given by the following function. If Linda still needs $576 , how many weeks has she been saving? How much money does Linda still need after 7 weeks?
A) first multiply 18 x 7 = 116, then subtract 500 - 116 = 384, so the answer is 384
B) first divide 384 from 18 which should give you 18, so the answer is 18
y^2 + 4 = x. for x the independent variable and the dependent variable. Determine whether the relation is a function.
Answer:
To determine if the given relation is a function, we need to check if there is a unique y-value for every x-value in the relation.
The given relation is:
y^2 + 4 = x
To test for functionality, we need to solve for y in terms of x:
y^2 = x - 4
y = ± √(x - 4)
Notice that for each x-value, there are two possible y-values, one positive and one negative. This means that for a single x-value, there are two potential y-values, violating the condition of a unique y-value for every x-value.
Therefore, the given relation is not a function since it fails the vertical line test, as there are x-values with multiple corresponding y-values.
What is the volume of this cylinder?
Use ≈ 3.14 and round your answer to the nearest hundredth.
--
10 yd
9 yd
The volume of the given cylinder is 2543 cubic yards.
For the given cylinder,
Height of the cylinder = 10 yard
Radius of cylinder = 9 yard yard
Then we have to calculate the volume of this cylinder.
Since we know that,
Volume of the cylinder = πr²h
Where,
r represents radius of cylinder = 9 yard
h represents height of cylinder = 10 yard
Noe therefore,
Volume of the cylinder = π(9)²(10)
= 3.14x 81 x 10
= 2543 cubic yards
Thus,
⇒ Volume = 2543 cubic yards.
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which expression can be used
Answer: The answer is A.
Step-by-step explanation: The surface area of a triangular prism is given by A = b h + ( b 1 + b 2 + b 3 ) l units 2 where is the base of a triangular face, is the height of a triangular face, , , and are the sides of the triangular base, and is the length of the prism.
The quilt is made of squares with diagonals.
The length of BD is 4.
a. Find the length of AE. Round answer to the hundredths.
b. Find the area of square ABCD.
The value 37 is a solution for the equation 3√√2 sece +7 = 1.
A. True
B. False
The statement that, the value 3π/4 is a solution for the equation 3√2 sec θ + 7 = 1 is true.
Given an equation,
3√2 sec θ + 7 = 1
We have to find that whether 3π/4 is a solution for the given equation or not.
Solving the given equation, we get,
3√2 sec θ + 7 = 1
3√2 sec θ = 1 - 7
3√2 sec θ = -6
sec θ = -6 / 3√2
sec θ = -2 / √2
sec θ = -√2
Now, we know that, sec θ = 1/ cos θ
So the equation becomes,
1/ cos θ = -√2
cos θ = -1/√2
Thus the solutions for the given equation are all values of θ such that cos θ = -1/√2.
cos 3π/4 = cos (π - π/4) = -cos (π/4) = -1/√2
So 3π/4 is a solution for the equation 3√2 sec θ + 7 = 1.
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Find the indicated angle
A.) 9
B.) 7
C.) 12
D.) 32
The calculated value of the missing side length in the triangle is (c) 12
How to find the indicated angleFrom the question, we have the following parameters that can be used in our computation:
The simiar triangles
Using the theorem of corresponding sides, we hav
?/8 = 9/6
Multiply both sides by 8
So, we have
? = 8 * 9/6
Evaluate
? = 12
Hence, the missing side length in the triangle is (c) 12
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El angulo en la base de un
triangulo ísósceles esde
34° la altura mide 15m
Calcular la longitud de los lados
iguales
It can be seen that each side of the isosceles triangle measures approximately 29.81 meters.
How to solveThe angles at the base of an isosceles triangle have equivalent magnitudes. It can be deduced intelligently that if one of the base angles measures 34°, the remaining base angle must also be 34°.
Let's denote the length of each side as "x."
In a right triangle formed by half of the base, the height, and one of the sides, we can use the tangent ratio:
tan(34°) = height / (x/2)
tan(34°) = 15 / (x/2)
To isolate x, we can rearrange the equation:
x/2 = 15 / tan(34°)
x = (15 / tan(34°)) * 2
By employing a calculator, we have the capability to determine the numerical worth of x.
x ≈ 29.81 m
Therefore, each side of the isosceles triangle measures approximately 29.81 meters.
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The question in English:
The angle at the base of an isosceles triangle 34° the height measures 15m
Calculate the length of the sides equal
Using a Net to Find the Surface Area of a Triangular Prism.
Answer:
Step-by-step explanation:
The measured width of the office is 30mm. If the scale of 1: 800 is used, calculate the actual width of the building in metres
Answer:
Step-by-step explanation:
Find the LCM of A= 3^2 x 5^4 x 7 and B= 3^4 x 5^3 x 7 x11
The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.
Given are two numbers which are showed in the prime factorized form.
A = 3² × 5⁴ × 7
B = 3⁴ × 5³ × 7 × 11
Prime factorization is the factorization of a number in terms of prime numbers.
In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.
A = 3² × 5³ × 5 × 7
B = 3² × 3² × 5³ × 7 × 11
Bring down the primes in each column.
LCM = 3² × 3² × 5³ × 5 × 7 × 11
= 3898125
Hence the LCM is 3898125.
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Can some one help me with this please
A) Area of figure is,
⇒ A = 3π (3 + √73) + 4.5π
B) Area of figure is,
A = 89 feet²
We can simplify as;
A) In figure A,
It is make with one cone and one semicircle.
Hence, Area of cone is,
A = πr (r + √h² + r²)
A = π × 3 (3 + √8² + 3²)
A = 3π (3 + √64 + 9
A = 3π (3 + √73)
And, Area of semicircle is,
⇒ A = 1/2 (π × 3²)
⇒ A = 4.5π
Hence, Total area is,
⇒ A = 3π (3 + √73) + 4.5π
B) Figure B is make with a trapezoid and triangle.
Area of trapezoid is,
A = 1/2 (7 + 13) × 5
A = 20 × 5 / 2
A = 50 feet²
And, Area of triangle is,
A = 1/2 × 6 × 13
A = 39 feet²
Hence, We get;
Area of figure is,
A = 50 + 39
A = 89 feet²
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a)
Shape 1 area is 753.8 cm³.
Shape 2 area 14.13 cm².
b)
Shape 1 area is 50 ft³.
Shape 2 area is 24 ft².
We have,
a)
The composite figure has a cone and a semicircle.
So,
Area of cone = 1/3πr²h = 1/3 x 3.14 x 3 x 3 x 8 = 753.8 cm³
Area of semicircle = 1/2 x πr² = 1/2 x 3.14 x 3 x 3 = 14.13 cm²
b)
The composite figure has a trapezium and a triangle.
Area of the trapezium
= 1/2 x ( sum of the parallel side) x h
= 1/2 x (7 + 13) x 5
= 1/2 x 20 x 5
= 10 x 5
= 50 ft³
Area of the triangle.
= 1/2 x base x height
= 1/2 x 6 x 8
= 3 x 8
= 24 ft²
Thus,
a)
Shape 1 area is 753.8 cm³.
Shape 2 area 14.13 cm².
b)
Shape 1 area is 50 ft³.
Shape 2 area is 24 ft².
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